Two investments in high- technology companies total $1,100. If one investment earns 10% annual interest and the other earns 10%, find the amount of each investment of the total interest earned is $140 for the year.
The value of the investment which earns 10% annual interest is $____ and the value of the investment which earns 20% annual is $______.
90
Let's solve this problem step by step.
Let's assume the amount invested in the first high-tech company that earns 10% annual interest is "x" dollars.
Therefore, the amount invested in the second high-tech company that earns 20% annual interest would be "1100 - x" dollars, as the total investment is $1100.
Now, let's calculate the interest earned by the first investment:
Interest = Principal * Rate
Interest1 = x * 0.10 = 0.10x
Similarly, let's calculate the interest earned by the second investment:
Interest2 = (1100 - x) * 0.20 = 0.20(1100 - x) = 220 - 0.20x
According to the problem, the total interest earned for the year is $140.
So, we can set up an equation:
Total interest = Interest1 + Interest2
140 = 0.10x + 220 - 0.20x
Now, let's solve this equation to find the value of "x":
140 = 0.10x + 220 - 0.20x
Combine like terms: 0.10x - 0.20x = -80
-0.10x = -80
Divide both sides by -0.10 to solve for "x":
x = -80 / -0.10
x = 800
So, the value of the investment that earns 10% annual interest is $800.
Now, we can substitute the value of "x" back into the total investment equation to find the value of the second investment:
Value of the second investment = 1100 - x
Value of the second investment = 1100 - 800
Value of the second investment = 300
Therefore, the value of the investment that earns 10% annual interest is $800, and the value of the investment that earns 20% annual interest is $300.